Gauge Field Theories on a Transverse Lattice

In these notes, the transverse ($\perp$) lattice approach is presented as a means to control the $k^{+}\to 0$ divergences in light-front QCD. Technical difficulties of both the canonical compact formulation as well as the non-compact formulation of the $\perp$ lattice motivate the color-dielectric formulation, where the link fields are linearized.